The locus in this screenshot is the image of the
dashed circle under 8 applications of the following function: a point
is inverted about each of the three points arranged in an equilateral
triangle in the center (inversion radius is the length of the segment
in the top left corner) and the new point is the centroid of the
triangle formed. (In case you're wondering where I got this function,
I did my highschool thesis
on analyzing a variant of it.)

This shows the benefit of adaptive sampling: the
locus is extremely non-uniform and without adaptive sampling, we
would see only a few points (even for many thousands of samples). As
it is, it looks acceptable on KSEG with 2000 samples (the screenshot
shows about 10000--and it looks perfect). With 2000 samples, KSEG can
redraw this locus a couple of times per second (on my 2 yr old
PII 350). I'd like to see another geometry program interactively
render a locus this complex! I won't even mention that this took me
less than four minutes to construct. Ok, I just did :-).
This file is included with the
examples as largelocus.seg. The construction used to generate it is
invert3.sec.